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How To Do xtabond2: An Introduction to Difference and System GMM in Stata

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Abstract

The difference and system generalized method-of-moments estimators, developed by Holtz-Eakin, Newey, and Rosen (1988, Econometrica 56: 1371-1395); Arellano and Bond (1991, Review of Economic Studies 58: 277-297); Arellano and Bover (1995, Journal of Econometrics 68: 29-51); and Blundell and Bond (1998, Journal of Econometrics 87: 115-143), are increasingly popular. Both are general estimators designed for situations with "small T , large N" panels, meaning few time periods and many individuals; independent variables that are not strictly exogenous, meaning they are correlated with past and possibly current realizations of the error; fixed effects; and heteroskedasticity and autocorrelation within individuals. This pedagogic article first introduces linear generalized method of moments. Then it describes how limited time span and potential for fixed effects and endogenous regressors drive the design of the estimators of interest, offering Stata-based examples along the way. Next it describes how to apply these estimators with xtabond2. It also explains how to perform the Arellano-Bond test for autocorrelation in a panel after other Stata commands, using abar. The article concludes with some tips for proper use. Copyright 2009 by StataCorp LP.

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... The Hansen test with a p-value above 0.05 does not reject the null hypothesis that instruments are uncorrelated with standard errors, confirming instrument validity in GMM. The Sargan statistic indicates no overidentification across all model estimates with a suggested cutoff value above 0.025 (Roodman, 2006). The number of instruments does not exceed the number of groups (<153). ...
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... The utilization of the System GMM estimator has enabled us to circumvent various issues that commonly arise in econometric analysis, such as (Roodman, 2009;Kapil & Kumar, 2023): the presence of fixed effects, heteroskedasticity and autocorrelation within individuals, the endogeneity of control variables, as well as the possible omission of variables that persist over time. To ensure the reliability and consistency of our econometric analysis, we have employed two diagnostic tests to evaluate the System GMM estimation. ...
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... The key difference between these approaches lies in the fact that instead of drawing assumptions about an entire distribution, the sGMM focuses on the specific moments (called moment conditions) of the random variables. Moreover, this approach is particularly effective when there is a large N and short T scenario (Blundell & Bond, 1998;Roodman, 2009). ...
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... However, Arellano and Bond (1991), Arellano-Bover (1995) and Blundell and Bond (1998) introduced the Generalized Method of Moments estimator (GMM), utilizing a comparable set of internal instruments which is more efficient compared to the Anderson and Hsiao (1981) estimator (Arellano & Bond, 1991;Arellano & Bover, 1995;Blundell & Bond, 1998). Therefore, to address the endogeneity issue, the study adopted the two-step system GMM (2SYSGMM) estimator for equation (21) following the approach by (Roodman, 2006). The effectiveness of the 2SYSGMM estimator is based on the validity and reliability of the instruments utilized. ...
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... The system GMM combines the regression in differences with the regression at levels in a system in which the two equations are instrumented separately (Arellano & Bond, 1998;Arellano & Bover, 1995). First, the system GMM does not suffer the problem of amplifying gaps originating from imbalanced panels, thus, the approach is resilient to problems related to unbalanced panels (Roodman, 2009). Second, it takes care of country-specific effects. ...
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... chi-square of the Breusch-Pagan test is greater than 0.05. Moreover, Table 6 demonstrates that the models are free from autocorrelation; the Durbin-Wats-stat is between 1 and 2. In addition, the study used generalized method of moments (GMM) estimations which account for heteroscedasticity and autocorrelation (Roodman, 2006). Furthermore, using a GMM estimate model tackles endogeneity issues. ...
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... We apply the system Generalized Method of Moments (GMM) estimation in order to address fundamental econometric issues such as the persistence of the outcome estimated variable, heteroskedasticity, endogeneity and unobserved heterogeneity. This panel econometric estimator permits the utilization of the exogenous regressors in the form of instrumental variables and lagged values of the dependent variable to control the problem of endogeneity, providing in this way more consistent and unbiased estimates than the traditional static panel estimators such as the OLS, fixed or/and random effects models (Wooldridge, 2010;Roodman, 2006;Windmeijer, 2005;Cameron & Trivedi, 2005). The system GMM specification, proposed by Blundell and Bond (Blundell & Bond, 1998), deploys moment conditions by combining the lagged first-differences of the regressors which are used as instruments for the level estimator of Arellano and Bover (Arellano & Bover, 1995) in addition with the appropriate lagged levels of regressors as instruments in the first-difference model estimator of Arellano and Bond (Arellano & Bond, 1991;Baltagi, 2013;Xu et al., 2011). ...
... Regarding variables that display a "random walk" or are near random-walk variables, the System GMM estimate is likewise superior to the Difference GMM (Baum, 2006;Bond, 2002;Roodman, 2007). Roodman (2006) recommends against using Difference GMM estimate since it has a flaw that makes gaps more noticeable when applied to unbalanced panels. The general form of the system GMM model is presented as. ...
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... In order to avoid the issue of excess instruments, the proliferation of instruments was limited, thus creating an instrument for each control variable instead of one instrument for each period and variable. This ensures that information is not lost and produces better results (Roodman, 2006). ...
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... Instead of drawing assumptions about the entire distribution, this model focuses on the specific moments (called moment conditions) of the random variables. This approach is particularly effective when there is a large N and short T scenario (Blundell & Bond, 1998;Roodman, 2009). ...
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... However, this estimator faces the issue of instruments proliferation. In order to contain this weakness, Roodman (2009) recommends specifying the model in such a way that the number of instruments does not exceed the number of countries. Similarly, for all our estimates, the standard errors are obtained via the correction proposed by Windmeijer (2005) for small sample. ...
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... This implies that the difference-GMM estimate is downward biased because of weak instrumentation and the system-GMM is preferred. System-GMM estimator is asymptotically efficient and robust to heteroskedasticity associated with serial correlation and autocorrelation since system-GMM assumes that differences are not correlated with the unobserved country effects (Ezeoha et al., 2015 andCoban andTopcu, 2013;Roodman, 2009aRoodman, , 2009bBond, 2002). We also use Windmeijer-corrected cluster robust errors to correct for the presence of cluster correlation. ...
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... panel estimator. The number of instruments is lower than the number of groups in the models suggesting no problem of instrument proliferation (Roodman, 2009). The insignificant value for AR (2 or 3) shows that there exists no issue of second or third order serial autocorrelation. ...
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... environmental sustainability in Asian economies. Three are three principal reasons to employ this technique for present analysis: First, the number of countries (N) is higher than the number of time period (T) (Roodman 2009), and this condition is satisfied in present case (N = 30 > T = 15). Second, system GMM estimators suggested by Blundell and Bond (1998) are used for present analysis because difference GMM estimator proposed by Arellano and Bover (1995) produced biased estimates in the case of small sample (Baltagi 2008). ...
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this paper and John Ham, David Hendry and members of the econometrics group at the London School of Economics for their useful comments on an earlier draft
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[eng] Transportation costs and monopoly location in presence of regional disparities. . This article aims at analysing the impact of the level of transportation costs on the location choice of a monopolist. We consider two asymmetric regions. The heterogeneity of space lies in both regional incomes and population sizes: the first region is endowed with wide income spreads allocated among few consumers whereas the second one is highly populated however not as wealthy. Among the results, we show that a low transportation costs induces the firm to exploit size effects through locating in the most populated region. Moreover, a small transport cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. [fre] Cet article d�veloppe une statique comparative de l'impact de diff�rents sc�narios d'investissement (projet d'infrastructure conduisant � une baisse mod�r�e ou � une forte baisse du co�t de transport inter-r�gional) sur le choix de localisation d'une entreprise en situation de monopole, au sein d'un espace int�gr� compos� de deux r�gions aux populations et revenus h�t�rog�nes. La premi�re r�gion, faiblement peupl�e, pr�sente de fortes disparit�s de revenus, tandis que la seconde, plus homog�ne en termes de revenu, repr�sente un march� potentiel plus �tendu. On montre que l'h�t�rog�n�it� des revenus constitue la force dominante du mod�le lorsque le sc�nario d'investissement privil�gi� par les politiques publiques conduit � des gains substantiels du point de vue du co�t de transport entre les deux r�gions. L'effet de richesse, lorsqu'il est associ� � une forte disparit� des revenus, n'incite pas l'entreprise � exploiter son pouvoir de march� au d�triment de la r�gion l
Article
This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation. The results also show that lagged hours is important in the hours equation. Copyright 1988 by The Econometric Society.
Does Foreign Direct Investment Accelerate Economic Growth? in T Does foreign direct investment promote development
  • M Carkovic
  • R Levine Moran
  • E M Graham
  • M Blomström
Carkovic, M., and R. Levine. 2005. Does Foreign Direct Investment Accelerate Economic Growth? in T.H. Moran, E.M. Graham, and M. Blomström. Does foreign direct investment promote development? Washington, DC: Institute for International Economics and Center for Global Development.
Enhanced routines for instrumental variables/generalized method of moments estimation and testing
–. 2007. Enhanced routines for instrumental variables/generalized method of moments estimation and testing. Stata Journal 7(4): 465-506.
  • F Hayashi
Hayashi, F. 2000. Econometrics. 1st ed. Princeton, NJ: Princeton University Press.
Classical Econometrics
  • P A Ruud
Ruud, P.A. 2000. Classical Econometrics. New York: Oxford University Press.